The measured intensities in an MR image, such as a brain image, are dependent on both the background noise and the local magnetic field. The degree of variation of the local magnetic fields at different locations in space is referred to as magnetic field inhomogeneity. Thus, the measured intensities of the image points can be different from the “true” intensities, which are the intensities one would have been obtained if there were no background noise and the magnetic field is homogenous, i.e. uniform over the imaged region. Field inhomogeneity can cause reduced image contrast and increased tissue variance. Thus, it is desirable to correct for the field inhomogeneity.
There are many conventional techniques for inhomogeneity correction. Typically, the measured image is segmented, either manually or automatically. The segmented image is then processed to estimate the inhomogeneity, represented as a map known as the inhomogeneity map.
For example, in one conventional technique, it is assumed that noise can arise randomly independent of the true image intensity but the field inhomogeneity contribution is dependent on the true image intensity. Thus, a measured image intensity (Im) can be expressed as:Im(x)=fb(x)It(x)+In(x),  (1)where x is the coordinate of the location of the image pixel or voxel, It is the true image intensity, In is the noise intensity, and fb is an unknown bias field, which may vary at different locations. Inhomogeneity correction thus involves estimating the bias field fb. In this technique, the bias field is assumed to be multiplicative and smoothly, slowly varying. The multiplicative bias field and the distribution of the true intensities are simultaneously estimated using an iterative approach, by maximizing the frequency content of the true intensity distribution.
Some conventional inhomogeneity correction techniques are discussed in B. Likar et al., “Retrospective correction of MR intensity inhomogeneity by information minimization”, IEEE Transactions on Medical Imaging, 2001, vol. 20, pp. 1398-1410; M. N. Ahmed et al., “A modified FCM algorithm for bias field estimation and segmentation of MRI data”, IEEE Transactions on Medical Imaging, 2002, vol. 21, pp. 193-199; B. Dawant et al. “Correction of intensity variations in MR images for computer-aided tissue classification”, IEEE Transactions on Medical Imaging, 1993, vol. 12, pp. 770-781; W. M. Wells et a/, “Adaptive segmentation of MRI data”, IEEE Transactions on Medical Imaging, 1996, vol. 15, pp. 429-442; R. Guillemaud and M. Brady, “Estimating the bias field of MR images”, IEEE Transactions on Medical Imaging, 1997, vol. 16, pp. 238-251; J. C. Rajapakse and F. Kruggel, “Segmentation of MR images with intensity inhomogeneities”, Image and Vision Computing, 1998, vol. 16, pp. 165-180; D. L. Pham and J. L. Prince, “Adaptive fuzzy segmentation of MR images”, IEEE Transactions on Medical Imaging, 1999, vol. 18, pp. 737-752; Sled et al., “A nonparametric method for automatic correction of intensity nonuniformity in MRI data”, IEEE Transactions on Medical Imaging, 1998, vol. 17, pp. 87-97; J. B. Arnold, J. S. Liow et al., “Qualitative and quantitative evaluation of six algorithms for correcting intensity nonuniformity effects”, NeuroImage, 2001, vol. 13, pp. 931-943.
However, conventional techniques have some drawbacks. One problem is that when the noise is relatively large, inhomogeneity correction obtained from these techniques is often inaccurate. Another problem is that it can take a relatively long time to complete an inhomogeneity correction using conventional techniques.